A346147 Primes p such that p*p' mod (p+p') and floor(p*p'/(p+p')) are prime, where p' is the next prime after p.
5, 11, 13, 113, 139, 157, 179, 193, 313, 359, 479, 509, 691, 773, 919, 953, 1019, 1039, 1093, 1453, 1571, 1873, 2297, 2341, 2357, 2459, 2633, 3089, 3229, 3253, 3571, 4021, 4219, 4483, 4523, 4663, 4889, 4933, 4943, 5113, 5153, 5179, 5233, 5261, 5323, 5449, 5591, 5639, 6037, 6073, 6079, 6337, 6373
Offset: 1
Keywords
Examples
a(3) = 13 is a term because 13 and 17 are consecutive primes with (13*17) mod (13+17) = 11 and floor(13*17/(13+17)) = 7 are prime.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
P:= select(isprime, [2,seq(i,i=3..10^5,2)]): f:= proc(n) local s,t; s:= P[n]+P[n+1]; t:= P[n]*P[n+1]; if isprime(t mod s) and isprime(floor(t/s)) then return P[n] fi end proc: map(f, [$1..nops(P)-1]);
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Mathematica
Select[Partition[Select[Range[6400], PrimeQ], 2, 1], PrimeQ[Mod[(p = First[#] * Last[#]), (s = First[#] + Last[#])]] && PrimeQ[Quotient[p, s]] &][[;; , 1]] (* Amiram Eldar, Jul 06 2021 *)
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PARI
list(lim)=my(v=List(),p=2,pq); forprime(q=3,nextprime(lim\1+1/2), pq=p*q; if(isprime(pq%(p+q)) && isprime(pq\(p+q)), listput(v,p)); p=q); Vec(v) \\ Charles R Greathouse IV, Jul 06 2021
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Python
from sympy import nextprime, isprime p, q, A346147_list = 2,3,[] while len(A346147_list) < 1000: if isprime(p*q % (p+q)) and isprime(p*q//(p+q)): A346147_list.append(p) p, q = q,nextprime(q) # Chai Wah Wu, Jul 06 2021
Comments